Problem: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{2}{15}-2\dfrac{8}{9} = {?}$
Find a common denominator for the fractions: $= {12\dfrac{6}{45}}-{2\dfrac{40}{45}}$ Convert ${12\dfrac{6}{45}}$ to ${11 + \dfrac{45}{45} + \dfrac{6}{45}}$ So the problem becomes: ${11\dfrac{51}{45}}-{2\dfrac{40}{45}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{51}{45}} - {2} - {\dfrac{40}{45}}$ Bring the whole numbers together and the fractions together: $= {11} - {2} + {\dfrac{51}{45}} - {\dfrac{40}{45}}$ Subtract the whole numbers: $=9 + {\dfrac{51}{45}} - {\dfrac{40}{45}}$ Subtract the fractions: $= 9+\dfrac{11}{45}$ Combine the whole and fractional parts into a mixed number: $= 9\dfrac{11}{45}$